Decay of turbulence generated by a square-fractal-element grid

A novel square-fractal-element grid was designed in order to increase the downstream measurement range of fractal grid experiments relative to the largest element of the grid. The grid consists of a series of square fractal elements mounted to a background mesh with spacing L₀ = 100\, mm . Measurements were performed in the region 3.5 ≤ x/L₀ ≤ 48.5 , which represents a significant extension to the x/L₀ < 20 of previously reported square fractal grid measurements. For the region x/L₀ 24 it was found that a power-law decay region following q² ~ (x - x₀)ᵐ exists with decay exponents of $m = -1.39$ and $-1.37$ at ReL₀ = 57\, 000 and $65\, 000$ , respectively. This agrees with decay values previously measured for regular grids ( -1 m -1.4 ). The turbulence in the near-grid region, x/L₀ < 20 , is shown to be inhomogeneous and anisotropic, in apparent contrast with previous fractal grid measurements. Nonetheless, power-law fits to the decay of turbulent kinetic energy in this region result in $m = -2.79$ , similar to m ≈ -2.5 recently reported by Valente & Vassilicos ( J. Fluid Mech. , vol. 687, 2011, pp. 300–340) for space-filling square fractals. It was also found that C_ε is approximately constant for x/L₀ ≥ 25 , while it grows rapidly for x/L₀ < 20 . These results reconcile previous fractal-generated turbulence measurements with classical grid turbulence measurements.